An adjoint method for second-order switching time optimization

Switched systems evolve over a sequence of continuous modes of operation, transitioning between modes in a discrete manner. Assuming a mode sequence is known, the evolution of a switched system is dictated by the set of times for which the modes transition. This paper presents second-order optimization of these switching times and compares its convergence with first-order switching time optimization. We emphasize the importance of the second-order method because it exhibits quadratic convergence and because even for relatively simple examples, first-order methods fail to converge on time scales compatible with real-time operation.